FWIW, I've only ever understood the four-legged animal to be a way of looking at how to move two connected people so that the other person is always kept balance deficient. You learn to connect (or not) to the other person, move them where there balance isn't and try to keep them there. To me, it's been something related too, but separate from what's going on in me.

As for going out and connecting to someones center and giving up your own, I'm pretty sure that obtuse way of going about things is only meant to be entry level. As soon as you're able to relaxedly connect to someone else, you have to start being just as aware of your own center as well. I've felt a few people at this point who were able to connect to me and put pressure on me without giving me any clear idea of where their center was and also put up resistance to me, making me feel like I was connected to them, but without giving up their balance to me. Essentially baiting me to give up more so they could take my balance.

I don't see how that's a bad thing. It becomes obvious pretty quickly, even against non-IS skilled people, that just making a connection isn't all there is to it.

It ...is....fine. I see it as just low entry level / high level- work. Sort of like trying to use the popular spinal wave for power generation. It is a step up from normal day-to-day work, but no where near the pinnacle of the bodies potential. Connecting centers will see you owned at speed against someone using a better model of retained center. You can't and will never be able to connect -to them- in the first place, so all else, all theory is for not. I continue to have people stare at me blank trying to figure out what I am doing, including the Chinese big dogs I was told to go test with.
I'm not trying to change your mind about anything. Most people in Aikido do your model. Some Aikido teachers out teaching "internal power" teach that "make connection" and change your insides model. Don't get me wrong. As I said earlier, with people less skilled than you it works. It "feels" great, even amazing for people who don't have IP/aiki. It softly controls, it moves and motivate others. It is very easy to be lulled into sticking with it and thinking it's the bee's knees. However, if those same teachers meet someone doing the model I am discussing -they will simply...lose. They will be reactive and late. It isn't even up for debate. It continuously happens over and over. It is made worse when and if the person retaining center knows how to smoothly make change over and over under stress and remain neutral within themselves, and worse still ...if they can fight with it.

The retained center relies on "no connection.' It is moving in accord with yin and yang freely and it becomes a difficult endeavor to find their center at all, in the process of which, yours is exposed and has to react. To further the point once again, it is the main thrust for solo training- spanning generations. The Japanese opted mostly for prearranged paired training. The result, was two very different approaches to power and control.
The fellow who argued for "I am the universe" understood what I am saying. So didn't three top level Chinese Taiji teachers.
Dan